What is the square root of 493

The short answer is \( \sqrt{ 493 } = 22.203603311175 \).

If that's all you're looking for, thanks for coming by. But if you're interested in the hows and whys behind square roots, continue reading and we'll tell you all about the square root of 493.

493 is not a perfect square

Let's look at some math

$$ \LARGE \sqrt{ 493 } = 22.203603311175 $$

Note that \(22.203603311175\) is not a whole number, therefore 493 is not a perfect square.

The next perfect square greater than 493 is 529. The previous perfect square less than 493 is 484.

Square root of 493 as an exponent

Any square root can be converted to a number with a fractional exponent. In the case of 493 the following two values are equal.

$$ \LARGE \sqrt{ 493 } = 493^{^1/_2} $$

Square root of 493 as a fraction

Since 493 is not a perfect square, sometimes we might want to get a fractional estimate of the square root value. In the case of 493 that value is \(\Large 22 \frac{11}{54}\).

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